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XPM-files, color channels can be extracted from images, images can be composed from color channels [1], [3].
4.3 3d-graphic objects
explicit(f(x,y),x,x1,x2,y,y1,y2)
Function f(x,y) within the ranges x1. . . x2 and y1. . . y2
implicit(equation,x,x1,x2,y,y1,y2,z,z1,z2)
Implizit curve defined by equation, in the variables x, y and z within the ranges x1. . . x2, y1. . . y2, z1. . . z2
parametric(x(t),y(t),z(t),t,t1,t2)
Parametric curve x(t),y(t),z(t) with the parameter t ranging from t1 to t2
parametric_surface(x(u,v),y(u,v),z(u,v),u,u1,u2,v,v1,v2)
Parametric surface x(u,v),y(u,v),z(u,v) with the parameters u and v within the ranges u1. . . u2 and v1. . . v2
cylindrical(r(z,ϕ),z,z1,z2,ϕ,ϕ1,ϕ2)
Surface in zylindric coordinates; radius r(z,ϕ) with respect to the z-coordinate z ranging from z1 to z2 and azimuth ϕ ranging from ϕ1 to ϕ2
spherical(r(ϕ,ϑ),ϕ,ϕ1,ϕ2,ϑ,ϑ1,ϑ2)
Surface in spherical coordinates; radius r(ϕ,ϑ) with respect to the azimuth ϕ ranging from ϕ1 to ϕ2 and the zenith ϑ ranging from ϑ1 to ϑ2
points(xvals,yvals,zvals) Points; xvals, yvals and zvals are lists containing the x-, y- and z-values respectively
points(p1,p2,...) Points; each point pi is a list containing its coordinates:
[px,py,pz].
label(["text",x,y,z],...) Text label text at the position [x,y,z]; alignment, font etc. can be set using options.
vector([x,y,z],[dx,dy,dz]) Vector with the origin [x,y,z] and its coordinates [dx,dy,dz]
3d-graphic objects
explicit and implicit define graphic objects by mathematical expressions in cartesian coordinates as surfaces in three-dimensional space. parametric defines a parametric curve with the parameter t, parametric_surface defines a surface in parametric form with two parameters u and v. cylindrical and spherical define a surface in cylindric and spheric coordinates respectively.
Contrary to the Gnuplot interface Plot, one single diagramm can contain any number of graphic objects.
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Sphere, defined as an implicit function
Two-dimensional function
Drawing the sphere and the two-dimensional function into one diagram. The option surface_hide supresses hidden parts.
Toroidal spiral as parametric curve with four windings around a toroid
Toroid as 3d-surface in parametric form
Common display of toroid and spiral
(%i37) gimp:implicit(1=x**2+y**2+z**2, x,-1,1,y,-1,1,z,-1,1);
€ Š
(%o37) implicit 1 = z2 + y2 + x2, x, −1, 1, y, −1, 1, z, −1, 1
(%i38) gexp:explicit(sin(2*x)*sin(2*y),x,-2,2,y,-2,2);
(%o38) explicit sin (2 x) sin 2 y , x, −2, 2, y, −2, 2
(%i39) wxdraw3d(surface_hide=true, color=red,gexp,color=blue,gimp)$
(%t39)
(%i40) spiral:parametric((2-0.5*cos(t))*sin(t/4), (2-0.5*cos(t))*cos(t/4), 0.5*sin(t),t,0,8*%pi);
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(%o40) parametric sin |
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(%i41) torus:parametric_surface( (2-0.2*cos(phi))*sin(theta), (2-0.2*cos(phi))*cos(theta), 0.2*sin(phi),phi,0,2*%pi,theta,0,2*%pi);
(%o41) |
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(%i42) |
wxdraw3d(nticks=200,surface_hide=true, |
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(%t42)
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Cone as a function in cylindric coordinates
Snail shell like surface, defined in spheric coordinates
Common display of cone and snail shell
3d-points in the xy-plane, shaping a circle
Four vectors, forming a compass rose
Texts in three-dimensional space; the text is not aligned to the axes, but to the view direction.
3d-graphic containing points, vectors and texts
(%i43) cone:cylindrical( (z-15)*0.05,z,-15,15,phi,0,2*%pi);
(%o43) cylindrical 0.05 (z − 15) , z, −15, 15, ϕ, 0, 2 π
(%i44) snail:spherical(4+0.5*phi,phi, -2*%pi,%pi,tht,0,%pi);
(%o44) spherical 0.5 ϕ + 4, ϕ, −2 π, π, tht, 0, π
(%i45) wxdraw3d(surface_hide=true,color=green,cone, color=brown,snail)$
(%t45)
(%i46) pts:points(makelist( [sin(t*%pi/10),cos(t*%pi/10),0],t,1,20))$
(%i47) [v1,v2,v3,v4]:[vector([0,0,1],[0.7,0,0]), vector([0,0,1],[0,0.7,0]),vector([0,0,1], [-0.7,0,0]),vector([0,0,1],[0,-0.7,0])];
(%o47) [vector ([0, 0, 1], [0.7, 0, 0]) , vector ([0, 0, 1], [0, 0.7, 0]) , vector ([0, 0, 1], [−0.7, 0, 0]) , vector ([0, 0, 1], [0, −0.7, 0])]
(%i48) text:label(["North",0,1,1],["East",1,0,1], ["South",0,-1,1],["West",-1,0,1]);
(%o48) label ([N or th, 0, 1, 1], [East, 1, 0, 1], [South, 0, −1, 1] , [West, −1, 0, 1])
(%i49) wxdraw3d(color=red,pts,color=orange, v1,v2,v3,v4,color=blue,text)$
(%t49)
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4.4 General Options
set_draw_defaults(opts,. . . ) Declares default values for options
terminal=term output format for the graphic; possible values: screen
(default), png, jpg, eps, eps_color, pdf.
file_name="file" output target for the graphic; default: maxima_out
user_preamble="text" Gnuplot preamble; contains arbitrary Gnuplot commands, which precede the actual plot process
dimensions=[width,height] Size of the graphic: in pixels for pixel graphics, in 1/10 mm for vector graphics
columns=n Number of columns for several scenes in one single graphic
color=colorname Line color
background_color=name Background color of the diagram
fill_color=name Fill color of rectangles, polygons and circles
x(yz)range=[min,max] Coordinate range of the x(yz)-axis
logx(yz)=true/false Logarithmic scale of the x(yz)-axis
grid=true/false Drawing grid lines, if true
x(yz)tics=true/false Controls the way tic marks are drawn on the x(yz)-axis x(yz)tics_rotate=true/false Determines, whether tic marks are rotated by 90◦
title="text" Main title for the scene (default: empty string)
key="text" Name of a function in the legend (def.: empty string)
x(yz)label="text" Label for the x(yz)-axis
x(yz)axis=true/false Determines,whether a x(yz)-axis is to be drawn
x(yz)axis_width=width Line width of the respective axis x(yz)axis_color=color Color of the respective axis
x(yz)axis_type=solid/dots Line type of the respective axis: solid line (solid) or dotted (dots), default: dots
line_width=width Line width
line_type=solid/dots Line type (default: solid)
point_size=size Point size in point-plots
point_type=n Point type, possible values: −1,0,1,2,. . . 13.
points_joined=true/false Determines, whether points are connected by line segments (default: false)
nticks=n Number of initial points used by the adaptive plotting routine (default: 30)
adapt_depth=n Maximum number of splittings used by the adaptive plotting routine (default: 10)
General plot options of the Gnuplot interface Draw
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set_draw_defaults declares default values for arbitrary options, calling that command with an empty parameter list (set_draw_defaults()), resets all options to their original default.
Options can be aggregated in lists, those lists can be included—even nested—into the parameter list of a plot command in place of single options.
terminal and file_name declare output format and output target of the graphic. Th possible output formats do not correspond to the Gnoplot terminals as stated in section 2.2. The file name (default: maxima_out) must not have an extension, the appropriate file extension (.eps,
.png, .jpg) will be added by Maxima automatically. Unless the path name is given, the file will be saved into the Gnuplot working directory. Declaring terminal or file_name within the wx-routines does not make sense and results in an error message.
The option user_preamble can contain any number of Gnuplot commands, separated by semicolons, as a text string. Hence settings can be passed to Gnuplot, which cannot be controlled by plot options (e. g. setting the aspect ratio of a diagram).
The option dimensions declares the size of the graphic. The values for height and width do not apply to the diagram, but o the entire graphic (or scene), including labels and margin (default:
[600,500]).
•Pixel graphics (png, jpg) are sized in pixels; the same holds true for the wx-routines (default: [500,300]).
•Vector graphics (eps, jpg) are sized in 1/10 mm.
Gnuplot preamble, graphic size, color and number of initial points are declared as default values for all subsequent graphics.
Options for supression of tick marks are put into a list.
Generation of a Lissajous curve as a parametric curve
Drawing the Lissajous curve using the new default options and an additional list of options
(%i50) |
set_draw_defaults( |
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nticks=200)$ |
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notics:[xtics=false,ytics=false]; |
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[x tics = f alse, y tics = f alse] |
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lissa:parametric(sin(3*t),sin(4*t),t,0,2*%pi); |
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parametric (sin (3 t) , sin (4 t) , t, 0, 2 π) |
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wxdraw2d(lissa,notics)$ |
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(%t53)
Resetting all default values |
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The option color and fill_color assign colors to all lines (outlines) and filled shapes, respectively; colors can be declared in hexadecimal form (#rrggbb) or by name according to the table below.
xrange, yrange and zrange are the displayed ranges in the respective coordinates in the form [min,max]. Their default values are false, in that case the displayed range will be calculated
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automatically. Setting the logx, logy and logz to true causes logarithmic scale of the respectice axes.
grid, xtics, ytics and ztics control the display of grid lines and tick marks on the axes. grid=true causes grid lines to be drawn at the tick marks. The value of xtics, ytics and zticks can be false (no ticks), true (tick marcs calculated automatically) or a set of values, at which tick marks (and grid lines, if applicable) are drawn:
x(yz)tics={w1,w2,. . . }
Each value can also be a list having two elements: a text string, which will be plotted, and a coordinate value for the position of that text string:
x(yz)tics={["text1",w1],["text2",w2],. . . }
The option x(yz)tics_rotate=true causes a rotation of the text strings by 90 degree.
title, xlabel, ylabel, zlabel and key produce labels for the axes and the entire diagram.
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light-green |
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black |
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Farbnamen f"ur das Gnuplot-Interface Draw
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Set of values for scale ticks along the y-axis and horizontal grid lines
Values for scale ticks along the x-axis and vertical grid lines as lists, each containing a text string and the x-coordinate
Sine curve with gridlines and tick marks
(%i55) yt:setify(create_list(signum(n) *sqrt(abs(n)),n,[-4,-3,-1,0,1,3,4])/2);
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(%i57) wxdraw2d(yrange=[-1.5,1.5],xtics=xt, ytics=yt,grid=true,color=red, explicit(sin(x),x,0,2*%pi), xlabel="phi (Grad)",ylabel="sin(phi)")$
(%t57)
Point plots (graphic object points) accept the option point_type with an integer value between −1 and 16 or a name according to the table below:
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square |
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filled_up_triangle |
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dot |
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filled_square |
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down_triangle |
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plus |
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circle |
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filled_down_triangle |
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multiply |
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filled_circle |
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diamant |
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asterisk |
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up_triangle |
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filled_diamant |
Possible values of the option point_type
Declaring points along a sine curve as a graphic object
(%i58) sine:points(float(map(lambda([u], [u,sin(u)]),makelist(u,u,-6,6)/2)));
(%o58) points([[−3.0, −0.141], [−2.5, −0.598], [−2.0, −0.909], [−1.5, −0.997], [−1.0, −0.841], [−0.5, −0.479], [0.0, 0.0], [0.5, 0.479], [1.0, 0.841], [1.5, 0.997], [2.0, 0.909], [2.5, 0.598], [3.0, 0.141]])
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Declaring points along a straight line as a graphic object
Sine function and two point plots: Points along the sine function, as well as points along a straight line, connected by line segments.
(%i59) line:points(float(makelist([k,-k/4],k,-3,3)));
(%o59) points([[−3.0, 0.75], [−2.0, 0.5], [−1.0, 0.25], [0.0, 0.0], [1.0, −0.25], [2.0, −0.5], [3.0, −0.75]])
(%i60) wxdraw2d(color=blue,line_width=2, explicit(sin(x),x,-%pi,%pi), color=red,point_size=2,point_type=7, sine,points_joined=true,point_type=4, color=green,line)$
(%t60)
4.5 Options for Labels and Vectors
label_alignment=value Alignment of the label; possible values: center (default), left, right
label_orientation=value Orientation of the label; possible values: horizontal (default), vertical
head_length=len Length of the arrowheads of vectors in units of the x-axis (default: 2)
head_angle=winkel Angle between arrow heads and segment in degrees (default: 45)
head_type=typ Type of the arrow head of vectors; possible values: filled (default), empty, nofilled
head_both=true/false Decides, whether vectors are plotted with two arrow heads
Options for labels and vectors
Three text strings
Assigning long option names to short variable names unburdens subsequent writing.
(%i61) [l1,l2,l3]:["left aligned label", "centered label","rigt aligned label"]$
(%i62) [la,hs,ha,hl]:[label_alignment, head_size,head_angle,head_length]$
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Vectors and variously aligned texts (%i63) wxdraw2d(xrange=[-1,1],yrange=[-6,5], yaxis=true,line_width=3,grid=true,la=left, label([l1,0,4]),la=center,label([l2,0,2]), la=right,label([l3,0,0]),ha=15,hl=0.2, color=red,vector([-0.5,-2],[0.5,0]), hl=0.3,color=blue,vector([-0.5,-4],[1,0]))$
(%t63)
4.6 Options for 2d-Graphics
axis_bottom=true/false The bottom axis is shown, if true (default).
axis_top=true/false The top axis is shown, if true (default).
axis_left=true/false The left axis is shown, if true (default).
axis_right=true/false The right axis is shown, if true (default).
filled_func=true/false The area between the plotted function and bottom axis is filled, if true.
filled_func=f The area between the plotted function and the function f is filled, if true.
transparent=true/false Polygons are colored according to the option fill_color, if true.
border=true/false Borders of polygons are painted, if true.
Options for 2d-graphics
List of options to supress axes and scale ticks
(%i64) noframe:[axis_left=false,axis_right=false, axis_top=false,axis_bottom=false, xtics=false,ytics=false]$
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Drawing various shapes with various |
(%i65) wxdraw2d(noframe,line_width=2, |
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(%t65)
Filling functions with colors |
(%i66) wxdraw2d(line_width=3,filled_func=true, |
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explicit( -0.5*sin(3*x),x,0,2*%pi))$ |
(%t66)
Wilhelm Haager: Graphics with MAXIMA